1. Field of the Invention
The present invention relates to a method, apparatus, and system for correction of phase distortion of waves. More particularly it relates the correction of air turbulence effects of electromagnetic waves.
2. Background Information
Waves are affected by passing through mediums. For example electromagnetic plane waves exhibit a phase shift while passing through fluids (e.g., the atmosphere) of differing indices of refraction. A signal will change as it traverses through a medium and knowing the phase effect of the medium, which can vary spatially and temporally, one can filter the medium's effect to acquire the original signal. For example one could filter out phase distortion effects of the medium and obtain clearer images.
In the fields of astronomy, free-space communications, and directed-energy applications a beacon (natural or artificial) is used to characterize the intervening atmospheric disturbances. The beacon emission is used to measure (wavefront detection) the turbulence-induced phase error, φ(t,x,y), created by the atmosphere. Deformable mirrors then correct the astronomical image, often involving incoherent radiation. Such correction allows for the astronomical imaging of dim stellar objects, since the noisy phase distortions have been removed. These astronomical techniques often involve post-processing, in which numerous images are averaged to reduce noise.
In free-space communications and directed-energy applications, typically involving coherent radiation, wavefront sensors and deformable mirrors actively correct the disturbance in real time. Systems involving real-time detection of wavefronts and correction can be complex and the equipment and computation can be expensive.
To avoid the use of deformable mirrors and expensive equipment researchers have sought to utilize the information available to a wavefront detector to correct the image digitally, i.e. modeling of the medium's effect on the traveling wave.
The correction of turbulence effects on electromagnetic waves requires real-time wavefront reconstruction. Some imaging systems, susceptible to atmospheric turbulence, having temporal time scales on the order of tens of Hertzs (e.g. 10 Hz), suffer from decreases in image resolution due to phase errors. A figure of merit indicating how quickly the atmospheric disturbances convect and evolve is the Greenwood frequency fG. The Greenwood frequency can be expressed as fG=(0.43)vw/r0, where vw is the wind speed, and r0 is the Fried coherence diameter. As mentioned above, atmospheric disturbances have frequencies on the order of tens of Hertzs. A correction system would have to sample and correct the phase distortions with a frequency greater than the Greenwood frequency of the disturbance.
In current imaging applications researchers have attempted to model the effect of atmospheric turbulence using a modulation transfer function, MTFturb=|H(f)|, that is spatially dependent on the turbulence size of eddy's (L0), the propagation constant “k”, the refractive-index structure Cn2, the spatial frequency ξ, the focal length “F”, the propagation path “z”, the wavelength λ, and the Fried diameter r0. One such transfer function is given as:
                              MTF          Turb                =                                                        H              ⁡                              (                f                )                                                          =                      {                                                                                ⅇ                                                                                            -                                                                                    (                                                              2.01                                ⁢                                                                                                                                  ⁢                                ξ                                ⁢                                                                                                                                  ⁢                                F                                ⁢                                                                                                                                  ⁢                                                                  λ                                  /                                                                      r                                    0                                                                                                                              )                                                                                      5                              /                              3                                                                                                      ,                                            ⁢                                                                                                                                                                                z                    >>                                                                  (                                                  0.4                          ⁢                                                      k                            2                                                    ⁢                                                      C                            n                            2                                                    ⁢                                                      L                            0                                                          5                              /                              3                                                                                                      )                                                                    -                        1                                                                                                                                                              1                    ,                                                                                        z                    ⁢                                          <<                                                                        (                                                      0.4                            ⁢                                                          k                              2                                                        ⁢                                                          C                              n                              2                                                        ⁢                                                          L                              0                                                              5                                /                                3                                                                                                              )                                                                          -                          1                                                                                                                                          }                                              (        1        )            
Often the impulse response function (IRF), which is the Fourier inverse of H(f), is use. The disadvantage of current modeled transfer functions is that they treat irregularities in a statistical manner. This does not allow the dynamic nature of atmospheric turbulence (irregularities) to be treated in a real time fashion. Hence H(f) is a function of frequency “f” but should in reality be treated as a function of time “t” as well (H(f,t)).
Hence a system/device/method, which avoids the use of wavefront sensors and deformable mirrors but takes into account the temporal nature of atmospheric irregularities to correct images is desirable.